International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 195-198
A note on conservative measures on semigroups
Department of Mathematics, University of Patra, Patra, Greece
Received 6 June 1990
Copyright © 1992 N. A. Tserpes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Consider the measure space where is a topological metric semigroup and a countably additive bounded Borel measure. Call conservative if all right translations , (which are assumed closed mappings) are conservative with respect in the ergodic theory sense. It is shown that the semigroup generated by the support of is a left group. An extension of this result is obtained for -finite .